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:<math>\phi_n (a) = a \otimes I_r,</math>
where ''I<sub>r</sub>'' is the identity in the ''r'' × ''r'' matrices. The sequence ...''k<sub>n</sub>''|''k<sub>n'' + 1</sub>|''k<sub>n'' + 2</sub>... determines a formal product
:<math>\delta(A) = \prod_p p^{t_p}</math>
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[[Category:C*-algebras]]
where each ''p'' is prime and ''t<sub>p</sub>'' = sup {''m''|''p<sub>m</sub>'' divides ''k<sub>n</sub> '' for some ''n''}, possibly zero or infinite. The formal product ''δ''(''A'') is said to be the '''
One example of a UHF C*-algebra is the [[CAR algebra]]. Its supernatural number is 2<sup>∞</sup>.
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